Context. Resonant planetary migration in protoplanetary discs can lead to an interplay between the resonant interaction of planets and their disc torques called overstability. While theoretical predictions and N-body simulations hinted at its existence, conclusive evidence was absent until subsequent hydrodynamical simulations were performed. Aims. Our primary purpose is to find a hydrodynamic setup that induces overstability in a planetary system with two moderate-mass planets in a first-order 2:1 mean motion resonance. Subsequently, we aim to analyse the impact of key disc parameters, namely viscosity, surface density, and aspect ratio, on the occurrence of overstability in this planetary system while keeping the mass of the planets constant. Methods. We performed 2D locally isothermal hydrodynamical simulations featuring two planets, with masses of 5 and 10 M⊕ , in a 2:1 resonance. Upon identifying the fiducial model where the system exhibits overstability, we performed simulations with different disc parameters to explore the effects of the disc on the overstability of the system. Results. We observed an overstable planetary system in our hydrodynamic simulations. In the parameter study, we noted that overstability occurs in discs characterised by low surface density and low viscosity. Increasing the surface density diminishes the possibility of overstability within the system. A limit cycle was observed in a specific viscous model with αν = 10−3 . In almost all our models, planets created partial gaps in the disc, which effects both the migration time scale and structure of the planetary system Conclusions. We demonstrate the existence of overstability using hydrodynamic simulations, but find deviations from the analytic approximation and show that main contribution to this deviation can be attributed to dynamic gap opening.

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